Equilibria and Rates

We have learned (Chap. 8) that some reactions occur under one set of conditions while an oppofcite reaction occurs under another set of conditions. For example, we learned that sodium and chlorine combine when treated with each other, but that molten NaCl decomposes when electrolyzed  

However, some sets of substances can undergo both a forward and a reverse reaction under the same set oi conditions. This circumstances leads to a state called chemical equilibrium. Before we take up equilibrium, however, we have to learn about the factors that affect the rate of a chemical reaction. 

In Chap. 8 heterogeneous catalysis was explained by postulating a three-step process (1) chemisorption of at least one reactant on the solid, (2) surface reaction of the chemisorbed substance, and (3) desorption of the product from the catalytic surface. Now our objective is to formulate rate and equilibrium equations for these steps. We shall consider the kinetics and equilibrium of adsorption and then examine rate equations for the overall reaction. 

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The rate of a reaction is defined as the change in concentration of any of its reactants or products per unit time. There are six factors that affect rate of a reaction  

The nature of the reactants. This factor is least controllable by the chemist. 

Temperature. In general, the higher the temperature of the system, the faster the chemical reaction will proceed. 

The presence of a catalyst. A catalyst is a substance that can accelerate a chemical reaction without undergoing a permanent change in its own composition. 

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A classic shock-tube study concerned the high-temperature recombination rate and equilibrium for methyl radical recombination [M, Ml- Methyl radicals were first produced in a fast decomposition of diazomethane at high temperatures (T > 1000 K)... 

Figure C2.7.2. Catalytic cycle (witliin dashed lines) for tire Wilkinson hydrogenation of alkene [2]. Values of rate and equilibrium constants are given in [2]...

A quantitative correlation between rate and equilibrium constants for the different metal ions is absent. The observed rate enhancements are a result of catalysis by the metal ions and are clearly not a result of protonation of the pyridyl group, since the pH s of all solutions were within the region where the rate constant is independent of the pH (Figure 2.1). 

The best-known equation of the type mentioned is, of course, Hammett s equation. It correlates, with considerable precision, rate and equilibrium constants for a large number of reactions occurring in the side chains of m- and p-substituted aromatic compounds, but fails badly for electrophilic substitution into the aromatic ring (except at wi-positions) and for certain reactions in side chains in which there is considerable mesomeric interaction between the side chain and the ring during the course of reaction. This failure arises because Hammett s original model reaction (the ionization of substituted benzoic acids) does not take account of the direct resonance interactions between a substituent and the site of reaction. This sort of interaction in the electrophilic substitutions of anisole is depicted in the following resonance structures, which show the transition state to be stabilized by direct resonance with the substituent ... 

Effects of Structure on Rate Electronic and steric effects influence the rate of hydra tion m the same way that they affect equilibrium Indeed the rate and equilibrium data of Table 17 3 parallel each other almost exactly... 

Many of the reactions listed at the beginning of this section are acid catalyzed, although a number of basic catalysts are also employed. Esterifications are equilibrium reactions, and the reactions are often carried out at elevated temperatures for favorable rate and equilibrium constants and to shift the equilibrium in favor of the polymer by volatilization of the by-product molecules. An undesired feature of higher polymerization temperatures is the increased probability of side reactions such as the dehydration of the diol or the pyrolysis of the ester. Basic catalysts produce less of the undesirable side reactions. 

LP Hammett. Some relations between reaction rates and equilibrium constants. Chem Rev 17 125-136, 1935. 

The dehydration reactions have somewhat higher activation energies than the addition step and are not usually observed under strictly controlled kinetic conditions. Detailed kinetic studies have provided rate and equilibrium constants for the individual steps in some cases. The results for the acetone-benzaldehyde system in the presence of hydroxide ion are given below. Note that is sufficiently large to drive the first equilibrium forward. 

When a Br nsted plot includes acids or bases with different numbers of acidic or basic sites, statistical corrections are sometimes applied in effect, the rate and equilibrium constants are corrected to a per functional group basis. If an acid has p equivalent dissociable protons and its conjugate base has q equivalent sites for proton addition, the statistically corrected forms of the Br insted relationships are... 

The equivalency of sites required for the application of these equations is seldom found in practice, although many authors apply these corrections. Benson has described an alternative procedure in which the rate and equilibrium constants are... 

Swain et al. ° analyzed solvent effects on 1080 pieces of rate and equilibrium data, showing that more than 98% of the effects could be correlated by the four-parameter equation... 

Summarizing, in order to calculate rate and equilibrium constants, we need to calculate and AGq. This can be done if the geometry, energy and force constants are known for the reactant, TS and product. The translational and rotational contributions are trivial to calculate, while the vibrational frequencies require the ftill force constant matrix (i.e. all energy second derivatives), which may involve a significant computational effort. 

The initial set of experiments and the first few textbook chapters lay down a foundation for the course. The elements of scientific activity are immediately displayed, including the role of uncertainty. The atomic theory, the nature of matter in its various phases, and the mole concept are developed. Then an extended section of the course is devoted to the extraction of important chemical principles from relevant laboratory experience. The principles considered include energy, rate and equilibrium characteristics of chemical reactions, chemical periodicity, and chemical bonding in gases, liquids, and solids. The course concludes with several chapters of descriptive chemistry in which the applicability and worth of the chemical principles developed earlier are seen again and again. 

Various successful Hammett LFER correlations of rate and equilibrium constants0... 

Thus, there is no great difficulty in accounting for each of the ions in Table IV the problem which remains is that of characterizing the rates and equilibrium constants of the various simultaneous reactions. 

Additional data were obtained from the study of kinetics of the slow disproportionation of the living dimers of methyl methacrylate. The progress of this reaction is shown in Fig. 8 which displays also the respective rates and equilibrium constants. 

Calculation of the second-order rate constant of carbonylation, kg, and the equilibrium constant, K = [t-C4H9CO+]/[t-C4H ][CO] = A c/fcD> requires knowledge of the concentration of CO. The constant a in Henry s law Pco = [CO] was determined to be 5-3 litre mole atm in HF—SbFs (equimolar) and 53 litre mole atm in FHSOs—SbFs (equimolar) at 20°C. From the ratio [t-C4HBCO+]/[t-C4HJ"] at a known CO pressure, values for k and K were obtained. The data are listed in Table 1, which includes the values for the rate and equilibrium constants of two other tertiary alkyl cations, namely the t-pentyl and the t-adamantyl ions (Hogeveen et al., 1970). 

It was desirable to test for possible inadequacy of the Oj values for certain substituents. This testing has been done with data for several reaction rate and equilibrium series for which both the p- and m- sets meet the minimal basis set requirements. The p and p/ values for the m- and p- positions obtained in preliminary fittings were held as constraints in the data, with the result that both Oj and Or values were generated from best fitting. 

The physical property measurements pertain to a specific state of chemical identity, whereas the rate and equilibrium measures pertain to a change between such states. Consequently, eq. (1) is shown to apply to either situation with essentially equal precision. The data sets with values appreciably... 

It is of interest that, as a consequence of the peculiar state of reactants in such systems, reactions rates and equilibrium constants are very often altered by several orders of magnitude as compared with those in homogeneous solution [114,115],... 

Writing unsteady-state component balances for each liquid phase results in the following pair of partial differential equations which are linked by the mass transfer rate and equilibrium relationships... 

For species 11 we will use the intrinsic barrier for hydroxide addition to trimethyl phosphate, G = 19 (calculated using rate and equilibrium data from reference 100) and assume the same value for the attack of hydroxide at sulfur on dimethyl sulfate. This (nonobservable) rate will be estimated using a Brpnsted type plot from the rate constants for diaryl sulfates (diphenyl sulfate,and bis p-nitrophenyl sulfate), estimated from the rate for phenyl dinitrophenyl sulfate,assuming equal contributions for the two nitro groups. This gives ftg = 0.95, and thus for dimethyl sulfate log k = 11.3... 

Chiang, Y. Kresge, J. Zhu, Y. Flash photolytic generation and study of /j-quinone methide in aqueous solution. An estimate of rate and equilibrium constants for heterolysis of the carbon-bromine bond in p-hydroxybenzyl bromide. J. Am. Chem. Soc. 2002,124, 6349-6356. 

Richard, J. P. Amyes, T. L. Bei, L. Stubblefield, V. The effect of beta-fluorine substituents on the rate and equilibrium-constants for the reactions of alpha-substituted 4-methoxybenzyl carbocations and on the reactivity of a simple quinone methide. J. Am. Chem. Soc. 1990, 112, 9513-9519. 

It appeared to the author some years ago that, irrespective of the mechanism of the toxic action of DDT, there might be a correlation of structure and toxicity in analogous compounds. Hammett (13) has shown that the rate and equilibrium constants of over 50 side-chain reactions of meta and para substituted aromatic compounds may be correlated with the so-called substituent constant a, according to the equation log k — log k0 = pa, where k and k0 are rate (or equilibrium) constants for substituted and unsubstituted compounds, respectively, p is the reaction constant giving the slope of the linear relationship, and a is the substituent constant, which is determined by the nature and... 

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